ML Aggarwal Algebra Exe-9.5 Class 6 ICSE Maths Solutions. We Provide Step by Step Answer of Exe-9.5 Questions for Algebra as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-6.

## ML Aggarwal Algebra Exe-9.5 Class 6 ICSE Maths Solutions

Board | ICSE |

Publications | Avichal Publishig Company (APC) |

Subject | Maths |

Class | 6th |

Chapter-9 | Algebra |

Writer | ML Aggarwal |

Book Name | Understanding |

Topics | Solution of Exe-9.5 Questions |

Edition | 2023-2024 |

**Algebra Exe-9.5**

**ML Aggarwal Class 6 ICSE Maths Solutions**

Page-198

**Question 1. State which of the following are equations with a variable. In case of an equation with a variable, identify the variable.**

(i) 17 + x = 5

(ii) 2b – 3 = 7

(iii) (y – 7) > 5

(iv) 9/3 = 3

(v) 7 × 3 – 19 = 2

(vi) 5 × 4 – 8 = 31

(vii) 2p < 15

(viii) 7 = 11 × 5 – 12 × 4

(ix) 3/2 q = 5

**Answer:**

(i) 17 + x= 5 Is an equation → L.H.S. = R.H.S. → Related variable x.

(ii) 2b – 3 = 7 Is an equation → L.H.S. = R.H.S. → Related variable b.

(iii) (y- 7) >5

Is not an equation → L.H.S. ≠ R.H.S.

It has no sign of equality (=).

(iv) 9/3 = 3

Is an equation = L.H.S. = R.H.S.

It has no variable.

(v) 7 × 3 – 19 = 2

Is an numerical equation = L.H.S. = R.H.S. It has no variable.

(vi) 5 × 4 – 8 = 31

Is an equation = L.H.S. = R.H.S. → Related variable t.

(vii) 2p < 15

Is not an equation = L.H.S. ≠ R.H.S.

It has no sign of equality.

(viii) 7 = 11 × 5 – 12 × 4

Is an numerical equation = L.H.S. = R.H.S. It has no variable.

(ix) 3/2 q = 5

Is an equation → L.H.S. = R.H.S. → Related variable q.

**Question 2.** Solve each of the following equations :

(i) x + 6 = 8

(ii) 2 – x = 5

(iii) 4x = -6

(iv) x/2 = 5

(v) 2y – 3 = 2

(vi) 4 – 5y = 2

**Answer:**

(i) x + 6 = 8

= x = 8 – 6 ⇒ x = 2

(ii) 2 – x = 5

= -x = 5 – 2 ⇒ -x = 3 ⇒ x = – 3

(iii) 4x = -6

(iv) x/2 = 5

= x = 5 × 2 ⇒ x = 10

(v) 2y – 3 = 2

= 2y = 2 + 3 ⇒ 2y = 5 ⇒ y = 5/2

(vi) 4 – 5y = 2

= 4 – 2 = 5y ⇒ 5y = 2

⇒ y = 2/5

**Question 3.** **Solve the following linear equations:**

(i) 5(x + 1) = 25

(ii) 2(3x – 1) = 10

(iii) (3x – 1)/4 = 11

**Answer:**

**(i) 5(x + 1) = 25**

⇒ 5(x + 1)/5 = 25/5 (dividing both sides by 5)

⇒ x + 1 = 5

⇒ x + 1 – 1 = 5 – 1 (Subtracting 1 from both sides)

⇒ x = 4

**(ii) 2(3x – 1) = 10**

⇒ 2(3x – 1)/2 = 10/2 (dividing both sides by 2)

⇒ 3x – 1 = 5

⇒ 3x – 1 + 1 = 5 + 1 (adding 1 to both sides)

⇒ 3x = 6

⇒ 3x/3 = 6/3 (dividing both sides by 3)

⇒ x = 2

(iii) Given (3x – 1)/4 = 11

⇒ 4 × (3x – 1)/4 = 4 × 11 (multiplying both sides by 4)

⇒ 3x – 1 = 44

⇒ 3x – 1 + 1 = 44 + 1 (adding 1 to both sides)

⇒ 3x = 45

⇒ 3x/3 = 45/3 (dividing both sides by 3)

⇒ x = 15

**Question 4. ****Solve the following linear equations:**

(i) 5x – 6 = 12 – x

(ii) n/3 + 1 = 4 – n

(iii) 5p + 7 = 19 – 2p

(iv) 2x + 5/2 = 2/3 -x

(v) x/2 -5 = x/3 -4

(vi) 18 – (3y/4) = 11 + y

**Answer:**

**(i) 5x – 6 = 12 – x**

⇒ 5x + x = 12 + 6

6x = 18 ⇒ x = 18/6 = 3

Verification

5x − 6 = 12 − x

⇒ 5(3) − 6 = 12 − 3

⇒ 15 – 6 = 9

⇒ 9 = 9

**(ii) n/3 + 1 = 4 – n**

**(iii) 5p + 7 = 19 – 2p **

⇒ 5p + 2p = 19 – 7

⇒ 7p = 12

⇒ p 12/7

Verification

**(iv) 2x + 5/2 = 2/3 -x**

**(v) x/2 – 5 = x/3 -4**

**(vi) 18 – (3y/4) = 11 + y**

**Question 5. Solve the following equations and verify your answers:**

(i) 3(x + 7) = 18

(ii) 2(x- 1) = x + 2

(iii) 3x – 1/2 = 2( x – 1/2) + 5

(iv) 4(2x – 1) -2(x – 5) = 5(x + 1) + 3

**Answer:**

**(i) 3(x + 7) = 18**

⇒ 3x + 21 = 18

⇒ 3x = 18 − 21

⇒ 3x = −3

⇒ x = -3/3

x = −1

Verification

⇒ 3(x + 7) = 18

⇒ 3(−1 + 7) = 18

⇒ 3(6) = 18

⇒ 18 = 18

**(ii) 2(x − 1) = x + 2**

⇒ 2x − 2 = x + 2

⇒ 2x − x = 2 + 2

⇒ x = 4

Verification

⇒ 2(x − 1) = x + 2

⇒ 2(4 − 1) = 4 + 2

⇒ 2(3) = 6

⇒ 6 = 6

**(iv) 4(2x – 1) -2(x – 5) = 5(x + 1) + 3**

⇒ 8x − 4 − 2x + 10 = 5x + 5 + 3

⇒ 8x − 2x− 4 + 10 = 5x + 5 + 3

⇒ 6x + 6 = 5x + 8

⇒ 6x – 5x = 8 – 6

⇒ x = 2

**Verification :**

4(2x − 1) − 2(x − 5) = 5(x + 1) + 3

⇒ 4 (2 × 2-1) – 2(2-5)=5(2+1)+3

⇒ 4 ( 4 – 1) – 2 (-3) = 5 ( 3) + 3

⇒ 4 ( 3) – 2 (-3) = 15 + 3

⇒ 12 + 6 = 18

⇒ 18 = 18

— : End of ML Aggarwal Algebra Exe-9.5 Class 6 ICSE Maths Solutions :–

Return to **–** ML Aggarwal Maths Solutions for ICSE Class -6

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